Quantum Tunneling — Double Barrier Resonance

Transfer matrix method — resonant tunneling when quasi-bound state aligns with incident energy

Barrier Parameters

Barrier height V₀ (eV) 1.0 Barrier width d (nm) 0.5 Well width w (nm) 1.0 Incident energy E (eV) 0.5

Adjust parameters…

Two rectangular barriers create a quasi-bound well state. When the incident energy matches a resonance energy, transmission T → 1 even though E < V₀.

T = |t|² via transfer matrix M = M_barrier · M_well · M_barrier

This is the operating principle of resonant tunneling diodes (RTDs). The transmission peaks are Breit-Wigner resonances with width Γ ∝ e^{-2κd}.

Above-barrier transmission also shows oscillatory structure from interference.